In complementarity theory, locally \(w\) -uniqueness property explains the dynamical system under unilateral constraint. The class of column competent matrices was studied extensively in this context. Motivated by locally \(w\) -uniqueness property, we introduce column competent tensor in the context of tensor complementarity problem. The tensor complementarity problem is a class of nonlinear complementarity problem with the involved function being defined by a tensor, which is also direct and natural extension of the linear complementarity problem. In the last few years, the tensor complementarity problem has been studied extensively from theory to solution methods and applications. In recent years, various tensors with special structures have been studied. For details see [1]}, [2]}. As an application of structured tensors, a class of nonlinear complementarity problem denoted as NCP, which is called the tensor complementarity problem denoted as TCP in[3]}, studied initially by Song and Qi[3]}. Different from studies in the case of NCP, properties of various structured tensors and the corresponding polynomial forms play important roles in the studies of TCP.
